### Abstract

If x, y, z are real numbers satisfying x + y + z = 1, then the maximum of the quadratic form axy + bxz + cyz with positive constants a, b, c is abc/2ab + 2ac + 2bc − a^{2} − b^{2} − c^{2} under the assumption √a < √b + √c. Extending this fact, we give the maximum of the quadratic form ∑1≤i<j≤n a_{ij}x_{i}x_{j} in n-variables x_{1}, …, x_{n} satisfying ∑^{n} _{i=1} x_{i} = 1 with constants a_{ij} = 0 under certain assumptions.

Original language | English |
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Pages (from-to) | 641-658 |

Number of pages | 18 |

Journal | Hokkaido Mathematical Journal |

Volume | 35 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 1 2006 |

Externally published | Yes |

### Keywords

- Distance matrix
- Ozeki’s inequality
- Quadratic form

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Izumino, S., & Nakamura, N. (2006). Maximization of quadratic forms expressed by distance matrices.

*Hokkaido Mathematical Journal*,*35*(3), 641-658. https://doi.org/10.14492/hokmj/1285766422